A two dimensional flow has velocities in x and y directions given by u = 2 xyt and v = -y²t, where t denotes time. The equation for streamline passing through x = 1, y = 1 is

Answer :

Solution :

u = 2xyt, v = -y²t

$\frac{dx}{2xyt}=\frac{dy}{-y^{2}t}\Rightarrow \int \frac{dx}{x}=-2\int \frac{dy}{y}$

In x = -2In y + ln C

ln x + ln y² = ln C

ln xy² = ln C

xy² = C

When equation for streamline passing through x = 1, y = 1 then C = 1

∴ xy² = 1 is the equation of streamline passing through x = 1, y = 1.